To live or visit?
Been to both a few times. I really like both, but it depends what you are looking for. For living both can be a bit cold, with Belgium probably slightly being the colder/more rainy of the two. Stuttgart is a younger crowd in an older city. There is a fairly large college there. Pretty cool outdoor shopping strip with places to eat and walk around. I've lucked out and hit really great weather pretty much my entire time at both. Every time I commented on the nice weather everyone told me it is never like that. That said, I'd happily move to either place. Belgium was a lot of fun. I've spent two weeks, mostly around Brussels with some time in Antwerp as well.